Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'An Introduction to Political Philosophy (Rev)' and 'Continuity and Irrational Numbers'

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45 ideas

5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A cut between rational numbers creates and defines an irrational number [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
If x changes by less and less, it must approach a limit [Dedekind]
7. Existence / A. Nature of Existence / 1. Nature of Existence
If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
Human beings can never really flourish in a long-term state of nature [Wolff,J]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Collective rationality is individuals doing their best, assuming others all do the same [Wolff,J]
Should love be the first virtue of a society, as it is of the family? [Wolff,J]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
For utilitarians, consent to the state is irrelevant, if it produces more happiness [Wolff,J]
Social contract theory has the attracton of including everyone, and being voluntary [Wolff,J]
Maybe voting in elections is a grant of legitimacy to the winners [Wolff,J]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
We can see the 'general will' as what is in the general interest [Wolff,J]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
How can dictators advance the interests of the people, if they don't consult them about interests? [Wolff,J]
24. Political Theory / C. Ruling a State / 3. Government / a. Government
'Separation of powers' allows legislative, executive and judicial functions to monitor one another [Wolff,J]
24. Political Theory / D. Ideologies / 1. Ideology
Political choice can be by utility, or maximin, or maximax [Wolff,J]
24. Political Theory / D. Ideologies / 2. Anarchism
A realistic and less utopian anarchism looks increasingly like liberal democracy [Wolff,J]
It is hard for anarchists to deny that we need experts [Wolff,J]
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
Utilitarianism probably implies a free market plus welfare [Wolff,J]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
A system of democracy which includes both freedom and equality is almost impossible [Wolff,J]
Democracy expresses equal respect (which explains why criminals forfeit the vote) [Wolff,J]
Democracy has been seen as consistent with many types of inequality [Wolff,J]
A true democracy could not tolerate slavery, exploitation or colonialism [Wolff,J]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
We should decide whether voting is for self-interests, or for the common good [Wolff,J]
Condorcet proved that sensible voting leads to an emphatically right answer [Wolff,J]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
Occasional defeat is acceptable, but a minority that is continually defeated is a problem [Wolff,J]
25. Social Practice / A. Freedoms / 4. Free market
Market prices indicate shortages and gluts, and where the profits are to be made [Wolff,J]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Liberty principles can't justify laws against duelling, incest between siblings and euthanasia [Wolff,J]
Either Difference allows unequal liberty, or Liberty makes implementing Difference impossible [Wolff,J]
25. Social Practice / B. Equalities / 1. Grounds of equality
Utilitarians argue for equal distribution because of diminishing utility of repetition [Wolff,J]
Difference Principle: all inequalities should be in favour of the disadvantaged [Wolff,J]
25. Social Practice / B. Equalities / 2. Political equality
Political equality is not much use without social equality [Wolff,J]
25. Social Practice / C. Rights / 1. Basis of Rights
If natural rights are axiomatic, there is then no way we can defend them [Wolff,J]
Standard rights: life, free speech, assembly, movement, vote, stand (plus shelter, food, health?) [Wolff,J]
If rights are natural, rather than inferred, how do we know which rights we have? [Wolff,J]
25. Social Practice / C. Rights / 4. Property rights
Utilitarians might say property ownership encourages the best use of the land [Wolff,J]
25. Social Practice / D. Justice / 1. Basis of justice
Rights and justice are only the last resorts of a society, something to fall back on [Wolff,J]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
Following some laws is not a moral matter; trivial traffic rules, for example [Wolff,J]